Approximate elliptical integral solution for the large amplitude free vibration of a rectangular single mode plate backed by a multi-acoustic mode cavity
作者： C.K. Hui , Y.Y. Lee , J.N. Reddy
DOI: 10.1016/J.TWS.2011.03.002
关键词: Finite element method 、 Nonlinear system 、 Geometry 、 Partial differential equation 、 Harmonic balance 、 Mathematics 、 Mathematical analysis 、 Harmonic (mathematics) 、 Vibration 、 Structural acoustics 、 Natural frequency
摘要: Abstract The nonlinear structural–acoustic problem considered in this study is the large amplitude free vibration of a rectangular elastic plate backed by cavity. Very few classical solutions for have been developed, although there are many or linear problems. Thus, main contributions paper include (1) concise multi-acoustic single structural modal formulation that derived from two coupled partial differential equations representing and acoustic pressure induced (2) approximate elliptical integral solution obtained solving one residual equation only, well agrees with harmonic balance finite element analysis. It found natural frequency convergences increase numbers modes terms, effects amplitude, air cavity depth, aspect ratio on also examined.
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